mathematics
Practice
sheets
BY TUSHAR CHOUDHARY
, TABLE OF CONTENTS
Chapter 01 APPLICATION OF DERIVATIVES
Chapter 02 APPLICATION OF INTEGRALS
Chapter 03 BASIC MATHEMATICS &
LOGARITHAM
Chapter 04 BINOMIAL THEOREM
Chapter 05 CIRCLE
Chapter 06 COMPLEX NUMBERS
Chapter 07 CONTINUITY
Chapter 08 DEFINITE INTEGRATION
Chapter 09 INDEFINITE INTEGRATION
Chapter 10 DETERMINANTS
Chapter 11 DIFFERENTIAL EQUATIONS
Chapter 12 ELLIPSE
Chapter 13 FUNCTIONS
Chapter 14 HYPERBOLA
, TABLE OF CONTENTS
Chapter 15 TRIGNOMETRIC RATIOS &
IDENTITIES
Chapter 16 INVERSE TRIGNOMETRIC
FUNCTIONS
Chapter 17 LIMITS OF FUNCTIONS
Chapter 18 MATRICES
Chapter 19 METHOD OF DIFFERENTIATION
Chapter 20 PARABOLA
Chapter 21 PERMUTATIONS & COMBINATION
Chapter 22 PROBABILITY
Chapter 23 QUADRATIC EQUATIONS
Chapter 24 SEQUENCE & SERIES
Chapter 25 SET THEORY & RELATIONS
Chapter 26 STATISTICS
Chapter 27 STRAIGHT LINES
Chapter 28 3-D GEOMETRY
Chapter 29 VECTOR ALGEBRA
, Application of Derivatives
Single Correct Type Questions 4. The function f(x) = xex(1–x), x ∈ is
1. Let f : (0, 1) → R be a function defined by 1
(a) Increasing in − ,1
2
1 and g(x) = (f(–x) – f(x)). Consider two
f ( x) =
1 − e− x 1
(b) Decreasing in , 2
statements [25 Jan, 2023 (Shift-I)] 2
(I) g is an increasing function in (0, 1)
1
(c) Increasing in −1, −
(II) g is one-one in (0, 1) 2
Then,
1 1
(a) Only (I) is true (d) Decreasing in − ,
2 2
(b) Only (II) is true
[28 July, 2022 (Shift-II)]
(c) Neither (I) nor (II) is true
5. The number of real solutions of x7 + 5x3 + 3x + 1 = 0 is
(d) Both (I) and (II) are true
equal to _______. [28 June, 2022 (Shift-I)]
2. Let f ( x=
) 2 x + tan x and g =
−1
( x ) loge ( 1+ x + x) , x
2 (a) 0
(b) 1
∈ [0, 3]. Then [1 February, 2023 (Shift-I)]
(a) There exists x ∈ [0, 3] such that f ′ ( x ) < g ′ ( x ) (c) 3
(b) max f(x) > max g(x) (d) 5
(c) There exist 0 < x1 < x2 < 3 such that f(x) < g(x), 6. Let f : R → R and g : R → R be two functions defined
∀x ∈ ( x1 , x2 ) 1 − 2e 2 x
by f(x) = loge (x2 + 1) – e–x + 1 and g ( x) = .
(d) min f ′ ( x ) = 1 + max g ′ ( x ) ex
Then, for which of the following range of a, the inequality
3. The surface area of a balloon of spherical shape being
( α − 1)2 5
inflated increases at a constant rate. If initially, the radius > f g α − holds ?
f g
of balloon is 3 units and after 5 seconds, it becomes 7 3 3
units, then its radius after 9 seconds is: [25 June, 2022 (Shift-I)]
[24 June, 2022 (Shift-I)]
(a) (2, 3)
(a) 9 (b) (–2, – 1)
(b) 10
(c) (1, 2)
(c) 11
(d) (–1, 1)
(d) 12
1 JEE PYQs Mathematics P
W
Practice
sheets
BY TUSHAR CHOUDHARY
, TABLE OF CONTENTS
Chapter 01 APPLICATION OF DERIVATIVES
Chapter 02 APPLICATION OF INTEGRALS
Chapter 03 BASIC MATHEMATICS &
LOGARITHAM
Chapter 04 BINOMIAL THEOREM
Chapter 05 CIRCLE
Chapter 06 COMPLEX NUMBERS
Chapter 07 CONTINUITY
Chapter 08 DEFINITE INTEGRATION
Chapter 09 INDEFINITE INTEGRATION
Chapter 10 DETERMINANTS
Chapter 11 DIFFERENTIAL EQUATIONS
Chapter 12 ELLIPSE
Chapter 13 FUNCTIONS
Chapter 14 HYPERBOLA
, TABLE OF CONTENTS
Chapter 15 TRIGNOMETRIC RATIOS &
IDENTITIES
Chapter 16 INVERSE TRIGNOMETRIC
FUNCTIONS
Chapter 17 LIMITS OF FUNCTIONS
Chapter 18 MATRICES
Chapter 19 METHOD OF DIFFERENTIATION
Chapter 20 PARABOLA
Chapter 21 PERMUTATIONS & COMBINATION
Chapter 22 PROBABILITY
Chapter 23 QUADRATIC EQUATIONS
Chapter 24 SEQUENCE & SERIES
Chapter 25 SET THEORY & RELATIONS
Chapter 26 STATISTICS
Chapter 27 STRAIGHT LINES
Chapter 28 3-D GEOMETRY
Chapter 29 VECTOR ALGEBRA
, Application of Derivatives
Single Correct Type Questions 4. The function f(x) = xex(1–x), x ∈ is
1. Let f : (0, 1) → R be a function defined by 1
(a) Increasing in − ,1
2
1 and g(x) = (f(–x) – f(x)). Consider two
f ( x) =
1 − e− x 1
(b) Decreasing in , 2
statements [25 Jan, 2023 (Shift-I)] 2
(I) g is an increasing function in (0, 1)
1
(c) Increasing in −1, −
(II) g is one-one in (0, 1) 2
Then,
1 1
(a) Only (I) is true (d) Decreasing in − ,
2 2
(b) Only (II) is true
[28 July, 2022 (Shift-II)]
(c) Neither (I) nor (II) is true
5. The number of real solutions of x7 + 5x3 + 3x + 1 = 0 is
(d) Both (I) and (II) are true
equal to _______. [28 June, 2022 (Shift-I)]
2. Let f ( x=
) 2 x + tan x and g =
−1
( x ) loge ( 1+ x + x) , x
2 (a) 0
(b) 1
∈ [0, 3]. Then [1 February, 2023 (Shift-I)]
(a) There exists x ∈ [0, 3] such that f ′ ( x ) < g ′ ( x ) (c) 3
(b) max f(x) > max g(x) (d) 5
(c) There exist 0 < x1 < x2 < 3 such that f(x) < g(x), 6. Let f : R → R and g : R → R be two functions defined
∀x ∈ ( x1 , x2 ) 1 − 2e 2 x
by f(x) = loge (x2 + 1) – e–x + 1 and g ( x) = .
(d) min f ′ ( x ) = 1 + max g ′ ( x ) ex
Then, for which of the following range of a, the inequality
3. The surface area of a balloon of spherical shape being
( α − 1)2 5
inflated increases at a constant rate. If initially, the radius > f g α − holds ?
f g
of balloon is 3 units and after 5 seconds, it becomes 7 3 3
units, then its radius after 9 seconds is: [25 June, 2022 (Shift-I)]
[24 June, 2022 (Shift-I)]
(a) (2, 3)
(a) 9 (b) (–2, – 1)
(b) 10
(c) (1, 2)
(c) 11
(d) (–1, 1)
(d) 12
1 JEE PYQs Mathematics P
W
